Haas got a wild card into the clay-court tournament and he could match or improve his best finish in Munich, where he was runner-up in 2000.
The 34-year-old German was once ranked as high as No. 2 but has dropped to No. 134 because of various injuries.
The fourth-seeded German defeated another Australian, qualifier Marinko Matosevic, 6-0, 7-6 (5).
Both Australians were in their first career quarterfinals on clay, Matosevic in his first tournament on the surface.